Extraction of $V_{ub}$ from the Decay $B\to πl ν$

We develop the perturbative QCD formalism including Sudakov effects for semi-leptonic $B$ meson decays. We evaluate the differential decay rate of $B\to πl ν$, and find that the perturbative calculation is reliable for the energy fraction of the pion above 0.3. Combining predictions from the soft pion theorems, we extract the value of the matrix element $|V_{ub}|$ which is roughly $2.7\times 10^{-3}$.

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